Question

Find the area of the quadrilateral, the coordinates of whose angular points taken In order are $(1,1),(3,4),(5,-2)$ and $(4,-7)$.

• A. $20.5$sq. units
• B. $41$ sq. units
• C. $82$ sq. units
• D. $61.5$ sq. units

Answer 1

The correct option is A $20.5$sq. units

Area of a polygon

$=\frac{1}{2}|(x_1{y}_2-y_1{x}_2)+(x_3{y}_4+x_4{y}_3)+....+(x_n{y}_1+y_n{x}_1)|=\frac{1}{2}\left|\right(4-3)+(-6-20)+(-35+8)+(4+7\left)\right|=\frac{1}{2}\left|41\right|=20.5$